Aline C. Soterroni

The q-gradient method for continuous global optimization

Here, we present an extension of the classical steepest descent method for solving global continuous optimization problems. To this end, we apply the concept of Jacksons derivative to compute the negative of the q-gradient of the objective function, used as the search direction. The use of Jacksons derivative has shown to be an effective mechanism for escaping from local minima. The q-gradient algorithm is complemented with strategies for selecting the parameter q and to compute the step length. These strategies are implemented in a way such that the search process gradually shifts from global in the beginning to local as the algorithm converges. For testing this new approach, we considered a set of multimodal test functions and compared our results with those obtained by Evolutionary Algorithms (EAs) widely used in optimizing multidimensional and multimodal functions. Overall, the q-gradient method performs well against the EAs arriving in forth position in a direct comparison with them, for the dimens...

The q-Gradient Vector for Unconstrained Continuous Optimization Problems

In the beginning of nineteenth century, Frank Hilton Jackson generalized the concepts of derivative in the q -calculus context and created the q -derivative, widely known as Jackson’s derivative. In the q -derivative, the independent variable is multiplied by a parameter q and in the limit, q → 1, the q -derivative is reduced to the classical derivative. In this work we make use of the first-order partial q -derivatives of a function of n variables to define here the q -gradient vector and take the negative direction as a new search direction for optimization methods. Therefore, we present a q -version of the classical steepest descent method called the q -steepest descent method, that is reduced to the classical version whenever the parameter q is equal to 1. We applied the classical steepest descent method and the q -steepest descent method to an unimodal and a multimodal test function. The results show the great performance of the q -steepest descent method, and for the multimodal function it was able to escape from many local minima and reach the global minimum.

The q-G method : A q-version of the Steepest Descent method for global optimization

AbstractIn this work, the q-Gradient (q-G) method, a q-version of the Steepest Descent method, is presented. The main idea behind the q-G method is the use of the negative of the q-gradient vector of the objective function as the search direction. The q-gradient vector, or simply the q-gradient, is a generalization of the classical gradient vector based on the concept of Jackson’s derivative from the q-calculus. Its use provides the algorithm an effective mechanism for escaping from local minima. The q-G method reduces to the Steepest Descent method when the parameter q tends to 1. The algorithm has three free parameters and it is implemented so that the search process gradually shifts from global exploration in the beginning to local exploitation in the end. We evaluated the q-G method on 34 test functions, and compared its performance with 34 optimization algorithms, including derivative-free algorithms and the Steepest Descent method. Our results show that the q-G method is competitive and has a great potential for solving multimodal optimization problems.

Modelling Land Use Change in Brazil:2000-2050 (Dataset)

The input and output land cover dataset across all modelled time periods (2000-2050) and scenarios resulting from the work of the REDD-PAC project in Brazil. Please consult the data section of the REDD-PAC website (http://redd-pac.org/new_page.php?contents=data1.csv) to access a data visualization tool and to obtain the dataset in WFS format. This dataset can be accessed and displayed using GIS software such as QGIS. Please consult the metadata file for further instructions

Using Models to inform Policies that meet multiple Objectives. Assessing the Contribution of Brazil's Forest Code to Biodiversity Conservation

Land-use change models can help to develop a holistic understanding of the range of potential impacts of different land-use related policy options, and so can strengthen development and implementation of policies to meet a range of objectives, including biodiversity conservation, climate change mitigation, sustainable development and food security. Brazil’s Native Vegetation Protection Act, commonly known as the Forest Code (FC), is one example of a policy that can be used to achieve several objectives. Using land-use modelling to inform ongoing decisions on how the provisions of the FC are put into practice can help to increase its effectiveness in meeting multiple objectives and commitments. Model projections show that the full implementation of the provisions of the FC will both reduce emissions of greenhouse gases and contribute to conserving biodiversity in Brazil. They further highlight the importance for biodiversity conservation of implementing the Environmental Reserve Tradable Certificate (CRA in Portuguese) mechanism quickly and effectively. Model results also show the need to put in place additional measures to protect areas, such as the Caatinga forests and grassy savanna in the Cerrado, which may suffer increased land-use pressures as a result of the FC.

Global optimization using q-gradients

The q-gradient vector is a generalization of the gradient vector based on the q-derivative. We present two global optimization methods that do not require ordinary derivatives: a q-analog of the Steepest Descent method called the q-G method and a q-analog of the Conjugate Gradient method called the q-CG method. Both q-G and q-CG are reduced to their classical versions when q equals 1. These methods are implemented in such a way that the search process gradually shifts from global in the beginning to almost local search in the end. Moreover, Gaussian perturbations are used in some iterations to guarantee the convergence of the methods to the global minimum in a probabilistic sense. We compare q-G and q-CG with their classical versions and with other methods, including CMA-ES, a variant of Controlled Random Search, and an interior point method that uses finite-difference derivatives, on 27 well-known test problems. In general, the q-G and q-CG methods are very promising and competitive, especially when applied to multimodal problems.

Método q-GC: uma generalização do método dos gradientes conjugados

Recentemente, baseado na derivada de Jackson, foi proposta uma generalizacao do metodo da maxima descida, denominada metodo do q-gradiente (q-G), para problemas de otimizacao global continua. Dentro desse contexto, este trabalho apresenta uma generalizacao do metodo dos gradientes conjugados (q-GC) com base no conceito do vetor q-gradiente. Para avaliar o desempenho do metodo q-GC foram considerados os resultados obtidos pelo metodo q-G e por tres Algoritmos Geneticos (AGs) para um conjunto de seis funcoes teste de 20 variaveis e mesmo criterio de parada. No geral, os resultados mostram que o q-GC ´e um metodo promissor para solucao de problemas de otimizacao multimodais.

Modelling Land Use Change in Brazil: 2000–2050

The input and output land cover dataset across all modelled time periods (2000-2050) and scenarios resulting from the work of the REDD-PAC project in Brazil. Please consult the data section of the REDD-PAC website (http://redd-pac.org/new_page.php?contents=data1.csv) to access a data visualization tool and to obtain the dataset in WFS format. This dataset can be accessed and displayed using GIS software such as QGIS. Please consult the metadata file for further instructions

Size Segregation in the Brazil Nut Effect

Granular materials are ubiquitous in nature and in our daily lives, and used in many industrial processes. Depending on the physical conditions that they are subjected, granular materials may present unusual behavior, combining properties of solids, liquids or gases, and displaying interesting and diversified phenomena. In this work we numerically simulated a granular system in order to investigate the phenomena of size segregation in the Brazil Nut Effect. Our simulations indicate that the phenomenon of size segregation results from the combined effect of two different mechanisms: buoyancy and convection. Increasing the vibration amplitude, the behavior of the system becomes less periodic and more turbulent, with evidence of deterministic chaos in the dynamics of the large particle.